Crop rotation for each field and the optional “RotationFields” program

The model requires one crop rotation per field. The allocation of a crop rotation per field, limits the possible spatial repartition of the crops over the landscape, particularly if the available crop rotations incorporate different crops. The crop rotations for each field might be provided by a survey carried out on the studied landscape. However, if the exact location of the rotation in the landscape is unknown or if new allocation of the rotations in the landscape must be tested, the user may use the “RotationFields” program.

The “RotationFields” program allocates the rotations to the fields. The user may specify either or both of the following parameters: (i) desired long-term proportion of any or all crops by area and the standard deviation permitted from the target, and (ii) the desired spatial patterns of the crop rotations. The spatial pattern is controlled by the statistical analysis based on the “E analysis” defined in Section 5.1.3.2 (General spatial trend (E analysis), p.57). Two other parameters are indispensable: the maximum number of iterations to obtain the allocation and the choice of using or not using weighted rotations to optimise the rotation allocation. The weighted rotation option is a preliminary step within the program, which alters the probability that a field is allocated any particular rotation, without considering the area of the field. (Areas are always considered within subsequent steps of the program). If the weighted rotation option is not used then each field has an equal probability of being allocated any of the rotations. If the weighted rotation option is selected, then each rotation is given a random weight, which affects accordingly its probability for being chosen for any field. The weighted rotations option is only useful if fields have relatively similar areas. It should also be noted that the use of the weighted rotation option may sometimes provide extreme allocations (e.g. if rotation x is given a weight of 95%, this rotation will be over-represented within the whole landscape).

Program inputs

- Possible crops in fields

- Rotation definitions as transition matrices

- Target long-term proportions of any crops + standard deviation permitted – not compulsory

- Target interval for the spatial pattern of crop rotations (Ep values, cf. Section 5.1.3.2: General spatial trend (E analysis), p.57) – not compulsory

- Maximum number of iterations

- The use, or not, of “weighted rotation” to optimize the allocation process

Program approach

The program goes through the following steps in order:

1. Crop rotations with a forbidden crop (i.e. long-crop proportion target equal to 0) are not considered within the program.

2. Each rotation is given an equal probability to be chosen when allocating a rotation to every field.

3. If “weighted rotations” was chosen, the above equal probabilities will be altered into uneven probabilities of choosing the rotations.

- Each rotation is given a random weight (the weight of all rotations adds up to 1).

- Calculate the long-term proportions of each crop with the current random weighing

- Check how many crop proportion targets are met.

- If more targets are met than the current best --> this current random weighting replaces the current best weighing.

- If less targets are met than the current best --> this current random weighing is deleted, and a new random weighting is created. This loop keeps on iterating until the maximum number of iterations is reached.

- If all targets of long-term crop proportions are met or if the maximum number of iteration is reached, the program proceeds to step 4.

4. For each field, the possible rotations are determined (using possible crops in fields) 5. For each field, a rotation is randomly allocated by using the rotation weights.

- If all targets of crop long-term proportions and spatial patterns are met --> the rotation allocation is accepted

- if not, the program goes to step 5 until the maximum number of iterations is reached.

Program outputs

- A rotation for each field

- Crop long-term proportions over the landscape of the rotation allocation

- Spatial pattern value (E and Ep) of the rotation allocation

7.2.6 Initial crops for each field and the optional “InitialCrops” program

The initial crops determine the crops, from the field crop rotation, to be grown in the first year of simulation. The coordination of the initial crops between fields influences the temporal patterns of the crops. An initial crop must be specified for every field. If they are not, then a random allocation option is available. If the random allocation option is activated, the “CropAllocation program” will randomly choose an initial crop when starting.

If the user wants to coordinate the initial crops between fields towards a specific crop temporal pattern, the InitialCrops program is available. The program will randomly allocate an initial crop to each field, and check if the current crops temporal patterns meet the requirements. The statistical analysis of the crops temporal pattern is based on the “Randomisation test of percentage of coefficient of variation of crops through time” defined in Chapter 5.1.2.3 (Crop temporal variability compared to random simulations, p.51).

Program inputs

- Number of randomisations for creating the randomization curve for the statistical test (default: 1,000 randomisations)

- Number of years on which the coefficient of variation is calculated (default: 100 years)

- Two choices of randomisation processes: after a failed allocation of initial crops to fields, the failed allocation has one initial crop altered (improve_ iteration) or all are re-randomised (random_iteration)

- Maximum number of iterations until allocation is accepted.

- Crop rotations as transition matrices

- Long-term crop proportions for each rotation

- A crop rotation per field

- Field areas

- Target interval for the temporal pattern of initial crops

Program approach

The program goes through the following steps chronologically:

1. The randomization curve for the temporal pattern analysis is created by using randomly allocated initial crops to each field.

3. If the current CVp value is within the targets
the current initial crop is accepted and the program stops.

4. If not, the iteration process starts:

5. If improve_ iteration was selected
a randomly chosen field has a new random initial crop.

6. If random_ iteration was selected
all the fields have new random initial crops. 7. The temporal pattern of the current initial crops is calculated

8. If the current CVp value is within the targets
the current initial crop is accepted and the program stops.

9. If not: the program goes to step 5.

Program outputs

- An initial crop for each field

- Temporal pattern value (%CV and CVp) of the rotation allocation

- Report on the iteration process